Biomedical subjects

E Ben-Naim

Publications and source records attributed to E Ben-Naim.

At least 19 recordsLinked to original sources

PubMed2006

Experimental characterization of vibrated granular rings.

We report an experimental study of the statistical properties of vibrated granular rings. In this system, a linked rod and bead metallic chain in the form of a ring is collisionally excited by a vertically oscillating plate. The dynamics are driven primarily by inelastic bead-plate collisions and are simultaneously constrained by the rings' physical connectedness. By imaging many instances of the ring configurations, we measure the ensemble averages and distributions of several physical characteristics on the scale of individual beads and composite ring. We study local properties such as inter-bead separation and inter-bonds angles, and global properties such as the radius of gyration and center-of-mass motion. We characterize scaling with respect to the size of the chain.

Colloids↗

PubMed2006

Alignment of rods and partition of integers.

We study dynamical ordering of rods. In this process, rod alignment via pairwise interactions competes with diffusive wiggling. Under strong diffusion, the system is disordered, but at weak diffusion, the system is ordered. We present an exact steady-state solution for the nonlinear and nonlocal kinetic theory of this process. We find the Fourier transform as a function of the order parameter, and show that Fourier modes decay exponentially with the wave number. We also obtain the order parameter in terms of the diffusion constant. This solution is obtained using iterated partitions of the integer numbers.

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PubMed2005

Power-law velocity distributions in granular gases.

The kinetic theory of granular gases is studied for spatially homogeneous systems. At large velocities, the equation governing the velocity distribution becomes linear, and it admits stationary solutions with a power-law tail, f (v) approximately v(-sigma) . This behavior holds in arbitrary dimension for arbitrary collision rates including both hard spheres and Maxwell molecules. Numerical simulations show that driven steady states with the same power-law tail can be realized by injecting energy into the system at very high energies. In one dimension, we also obtain self-similar time-dependent solutions where the velocities collapse to zero. At small velocities there is a steady state and a power-law tail but at large velocities, the behavior is time dependent with a stretched exponential decay.

Journal Article↗

PubMed2005

Velocity distributions of granular gases with drag and with long-range interactions.

We study velocity statistics of electrostatically driven granular gases. For two different experiments, (i) nonmagnetic particles in a viscous fluid and (ii) magnetic particles in air, the velocity distribution is non-Maxwellian, and its high-energy tail is exponential, P(upsilon) approximately exp(-/upsilon/). This behavior is consistent with the kinetic theory of driven dissipative particles. For particles immersed in a fluid, viscous damping is responsible for the exponential tail, while for magnetic particles, long-range interactions cause the exponential tail. We conclude that velocity statistics of dissipative gases are sensitive to the fluid environment and to the form of the particle interaction.

Air Movements↗

PubMed2005

Stationary states and energy cascades in inelastic gases.

We find a general class of nontrivial stationary states in inelastic gases where, due to dissipation, energy is transferred from large velocity scales to small velocity scales. These steady states exist for arbitrary collision rules and arbitrary dimension. Their signature is a stationary velocity distribution f(v) with an algebraic high-energy tail, f(v) approximately v(-sigma). The exponent sigma is obtained analytically and it varies continuously with the spatial dimension, the homogeneity index characterizing the collision rate, and the restitution coefficient. We observe these stationary states in numerical simulations in which energy is injected into the system by infrequently boosting particles to high velocities. We propose that these states may be realized experimentally in driven granular systems.

Journal Article↗

PubMed2005

Kinetic theory of random graphs: from paths to cycles.

The structural properties of evolving random graphs are investigated. Treating linking as a dynamic aggregation process, rate equations for the distribution of node to node distances (paths) and of cycles are formulated and solved analytically. At the gelation point, the typical length of paths and cycles, l , scales with the component size k as l approximately k(1/2) . Dynamic and finite-size scaling laws for the behavior at and near the gelation point are obtained. Finite-size scaling laws are verified using numerical simulations.

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PubMed2005

Granular chains.

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Journal Article↗

PubMed2004

Size of outbreaks near the epidemic threshold.

The spread of infectious diseases near the epidemic threshold is investigated. Scaling laws for the size and the duration of outbreaks originating from a single infected individual in a large susceptible population are obtained. The maximal size of an outbreak n(*) scales as N(2/3) with N the population size. This scaling law implies that the average outbreak size [n]scales as N(1/3). Moreover, the maximal and the average duration of an outbreak grow as t(*) approximately N(1/3) and [t] approximately ln N, respectively.

Communicable Diseases↗

PubMed2004

Finite-size fluctuations in interacting particle systems.

Fluctuations may govern the fate of an interacting particle system even on the mean-field level. This is demonstrated via a three species cyclic trapping reaction with a large, yet finite number of particles, where the final number of particles N(f) scales logarithmically with the system size N, N(f) approximately ln N. Statistical fluctuations, that become significant as the number of particles diminishes, are responsible for this behavior. This phenomenon underlies a broad range of interacting particle systems including in particular multispecies annihilation processes.

Journal Article↗

PubMed2003

Exchange-driven growth.

We study a class of growth processes in which clusters evolve via exchange of particles. We show that depending on the rate of exchange there are three possibilities: (I) Growth-clusters grow indefinitely, (II) gelation-all mass is transformed into an infinite gel in a finite time, and (III) instant gelation. In regimes I and II, the cluster size distribution attains a self-similar form. The large size tail of the scaling distribution is Phi(x) approximately exp(-x(2-nu)), where nu is a homogeneity degree of the rate of exchange. At the borderline case nu=2, the distribution exhibits a generic algebraic tail, Phi(x) approximately x(-5). In regime III, the gel nucleates immediately and consumes the entire system. For finite systems, the gelation time vanishes logarithmically, T approximately [lnN](-(nu-2)), in the large system size limit N--> infinity. The theory is applied to coarsening in the infinite range Ising-Kawasaki model and in electrostatically driven granular layers.

Journal Article↗

PubMed2003

Shattering transitions in collision-induced fragmentation.

We investigate the kinetics of nonlinear collision-induced fragmentation. We obtain the fragment mass distribution analytically by utilizing its traveling wave behavior. The system undergoes a shattering transition in which a finite fraction of the mass is lost to infinitesimal fragments (dust). The nature of the shattering transition depends on the fragmentation process. When the larger of the two colliding fragments splits, the transition is discontinuous and the entire mass is transformed into dust at the transition point. When the smaller fragment splits, the transition is continuous with the dust gaining mass steadily on the account of the fragments. At the transition point, the fragment mass distribution diverges algebraically for small masses, c(m) approximately m(-alpha), with alpha=1.201 91 em leader.

Journal Article↗

PubMed2002

Entropic tightening of vibrated chains.

We investigate experimentally the distribution of configurations of a ring with an elementary topological constraint, a "figure-8" twist. Using a system far from thermal equilibrium, a vibrated granular chain, we show that configurations where one loop is small and the second is large are strongly preferred. Despite the highly non-equilibrium nature of the system, our results are consistent with recent predictions for equilibrium properties of topologically-constrained polymers. The dynamics of the tightening process weakly violates a (coarse-grained) detailed balance, indicating that the unexpected correspondence with an equilibrium entropic approach is not exact.

Journal Article↗

PubMed2002

Scaling, multiscaling, and nontrivial exponents in inelastic collision processes.

We investigate velocity statistics of homogeneous inelastic gases using the Boltzmann equation. Employing an approximate uniform collision rate, we obtain analytic results valid in arbitrary dimension. In the freely evolving case, the velocity distribution is characterized by an algebraic large-velocity tail, P(v,t) approximately v(-sigma). The exponent sigma(d,epsilon), a nontrivial root of an integral equation, varies continuously with the spatial dimension d and the dissipation coefficient epsilon. Although the velocity distribution follows a scaling form, its moments exhibit multiscaling asymptotic behavior. Furthermore, the velocity autocorrelation function decays algebraically with time, A(t)= approximately t(-alpha), with a nonuniversal dissipation-dependent exponent alpha=1/epsilon. In the forced case, the steady state Fourier transform is obtained via a cumulant expansion. Even in this case, velocity correlations develop and the velocity distribution is non-Maxwellian.

Journal Article↗

PubMed2002

Impurity in a Maxwellian unforced granular fluid.

We investigate velocity statistics of an impurity immersed in a uniform granular fluid. We consider the cooling phase, and obtain scaling solutions of the inelastic Maxwell model analytically. First, we analyze identical fluid-fluid and fluid-impurity collision rates. We show that light impurities have similar velocity statistics as the fluid background, although their temperature is generally different. Asymptotically, the temperature ratio increases with the impurity mass, and it diverges at some critical mass. Impurities heavier than this critical mass essentially scatter off a static fluid background. We then analyze an improved inelastic Maxwell model with collision rates that are proportional to the average fluid-fluid and fluid-impurity relative velocities. Here, the temperature ratio remains finite, and the system is always in the light-impurity phase. Nevertheless, ratios of sufficiently high-order moments / may diverge, a consequence of the multiscaling asymptotic behavior.

Journal Article↗

PubMed2001

Extremal properties of random trees.

We investigate extremal statistical properties such as the maximal and the minimal heights of randomly generated binary trees. By analyzing the master evolution equations we show that the cumulative distribution of extremal heights approaches a traveling wave form. The wave front in the minimal case is governed by the small-extremal-height tail of the distribution, and conversely, the front in the maximal case is governed by the large-extremal-height tail of the distribution. We determine several statistical characteristics of the extremal height distribution analytically. In particular, the expected minimal and maximal heights grow logarithmically with the tree size, N, h(min) approximately v(min) ln N, and h(max) approximately v(max) ln N, with v(min)=0.373365ellipsis and v(max)=4.31107ellipsis, respectively. Corrections to this asymptotic behavior are of order O(ln ln N).

Journal Article↗

PubMed2001

Knots and random walks in vibrated granular chains.

We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard-core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with theoretical values.

Journal Article↗

PubMed2000

Multiscaling in inelastic collisions

We study relaxation properties of two-body collisions on the mean-field level. We show that this process exhibits multiscaling asymptotic behavior as the underlying distribution is characterized by an infinite set of nontrivial exponents. These nonequilibrium relaxation characteristics are found to be closely related to the steady state properties of the system.

Journal Article↗

PubMed2000

Scale invariance and lack of self-averaging in fragmentation

We derive exact statistical properties of a recursive fragmentation process. We show that introducing a fragmentation probability 0<p<1 leads to a purely algebraic size distribution, P(x) approximately x(-2p), in one dimension. In d dimensions, the volume distribution diverges algebraically in the small fragment limit, P(V) approximately V-gamma, with gamma=2p(1/d). Hence, the entire range of exponents allowed by mass conservation is realized. We demonstrate that this fragmentation process is non-self-averaging as the moments Y(alpha)= summation operator(i)x(alpha)(i) exhibit significant sample to sample fluctuations.

Journal Article↗